Although the PCL problem has a solid theoretical grounding, the question of how to estimate the causal effect remains a practical challenge, in particular when we consider nonlinear causal relationships or high-dimensional treatments. In [1]}, the treatment and outcome are assumed to be categorical variables. In a follow-up study, [2]} show that we can learn a linear causal effect by a method of moments. [3]} models the causal effect as a linear combination of nonlinear basis functions, which is learned by solving two stage regression. These two methods are extended in Mastouri and Zhu et al. [4]}, who learn the causal effect in a predefined reproducing kernel Hilbert space (RKHS). We provide an overview of the PCL problem and the two-stage regression in Section . Although these methods enjoy desirable theoretical properties, the flexibility of the model is limited, since all existing work uses pre-specified features.
